In our experiment of the Poisson equation, where we can directly compare to traditional PINNs, we observe that is possible to obtain similar levels of errors, showing that our method can also be used for simple domains. Furthermore, we did not see a decrease in performance when we compared the numerically obtained eigenfunctions versus the exact ones. The number of eigenfunctions used did alter the accuracy of our method. This quantity is a common hyper-parameter that needs to be tuned in some sort of shape for all positional encodings [1]}. We also observed that the size of the discretization to compute the operators also has an impact on the accuracy in a non-monotonic fashion. The way that changing the discretization affects the loss landscape and the training process requires further studies, which we believe are beyond the scope of this work.
